Solve y=2(1/3y-1/3)+5

$$y=2( \frac{ 1 }{ 3 } y- \frac{ 1 }{ 3 } )+5$$

Solve for y

$$y=13$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by \frac{1}{3}y-\frac{1}{3}.

$$y=2\times \frac{1}{3}y+2\left(-\frac{1}{3}\right)+5$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$y=\frac{2}{3}y+2\left(-\frac{1}{3}\right)+5$$

Express 2\left(-\frac{1}{3}\right) as a single fraction.

$$y=\frac{2}{3}y+\frac{2\left(-1\right)}{3}+5$$

Multiply 2 and -1 to get -2.

$$y=\frac{2}{3}y+\frac{-2}{3}+5$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$y=\frac{2}{3}y-\frac{2}{3}+5$$

Convert 5 to fraction \frac{15}{3}.

$$y=\frac{2}{3}y-\frac{2}{3}+\frac{15}{3}$$

Since -\frac{2}{3} and \frac{15}{3} have the same denominator, add them by adding their numerators.

$$y=\frac{2}{3}y+\frac{-2+15}{3}$$

Add -2 and 15 to get 13.

$$y=\frac{2}{3}y+\frac{13}{3}$$

Subtract \frac{2}{3}y from both sides.

$$y-\frac{2}{3}y=\frac{13}{3}$$

Combine y and -\frac{2}{3}y to get \frac{1}{3}y.

$$\frac{1}{3}y=\frac{13}{3}$$

Multiply both sides by 3, the reciprocal of \frac{1}{3}.

$$y=\frac{13}{3}\times 3$$

Cancel out 3 and 3.

$$y=13$$